<TITLE>prob004: mystery shopper</TITLE>
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<CENTER>
<H1>prob004: mystery shopper</H1>

<TABLE>
<TR> <TD> proposed by
     <TD ALIGN=LEFT> <A HREF="http://www.cs.cuhk.hk/~jlee/">
          <B>Jim Ho Man Lee</B></A> 
          <ADDRESS><a href="mailto:jlee@cs.cuhk.hk">
          jlee@cs.cuhk.hk</a></ADDRESS>
</TABLE>
</CENTER>
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<H3> Specification </H3>
<TT>
A well-known cosmetic company wants to evaluate the performance of her 
saleladies, who station at the company's counters at various department
stores in different geographical locations.  For this purpose, the 
company has hired some secret agents to disguise as shoppers to visit 
the salesladies.  The visits must be scheduled in such a way that each 
saleslady must be visited by shoppers of different varieties and that 
the visits should be spaced out roughly evenly.  Also, shoppers should 
visit salesladies in different geographic locations.  The exact constraints, 
which ensure the statistical soundness of the project, follow.
<P>

1. There are totally 19 outlets to be visited. They are located in 4
   geographical regions:
   5 outlets in Area 1 (outlet 1-5), 
   5 outlets in Area 2 (outlet 6-10),
  5 outlets in Area 3 (outlet 11-15),
  and 4 outlets in Area 4 (outlet 16-19).

<P>
2. There will be 1 to 4 salesladies in each outlet.  Each saleslady will 
   be visited by 4 different shoppers. The frequency of visits to a 
   particular outlet will be the number of salesladies times 4.  There are 
   totally 35 salesladies working in all outlets everyday.  Therefore,
   the total number of visits is 140.
<P>

3. The shoppers are divided into 4 groups according to age, professions,
   and etc.  Each group has 10 shoppers. Therefore, the total number 
   of shoppers is 40.  Therefore, in each group of shoppers, 5 shoppers
   will perform 3 visits and the other 5 shoppers will perform 4 visits.
<P>

4. Each shopper should only visit 1 outlet in each of the 4 areas.

<P>
5. All salesladies should be visited 2 times in the first 2 weeks of
   fieldwork.

<P>
6. The total fieldwork period will be 4 weeks. Theoretically, each
   shopper has to pay 1 visit each week. However, shoppers making 4 visits
   must have done 2 visits by the end of the second week.  Shoppers making
   3 visits should have done 1 or 2 visits by the end of the second week.
   The data of the first 50% visits will be analysed and put in an interim 
   report.
<P>

7. Listed below are locations of the 19 outlets and the number of
   salesladies in that particular outlet. (outlets with * are boutiques)
<P>

<CENTER>
<TABLE>
<TD>
    Outlet  <TD>                                     Number of Salesladies <TR>
<TD>   ====== <TD>                                     ===================== <TR>
<TR> <TD>   *Outlet 1 <TD>                                         2
<TR> <TD>    Outlet 2              <TD>                              4
<TR> <TD>    Outlet 3                  <TD>                          1
<TR> <TD>    Outlet 4                      <TD>                      2
<TR> <TD>    Outlet 5                 <TD>                           1
<TR> <TD>    Outlet 6                     <TD>                       2
<TR> <TD>    Outlet 7                         <TD>                   1
<TR> <TD>    Outlet 8                             <TD>               1
<TR> <TD>    Outlet 9                                 <TD>           1
<TR> <TD>   *Outlet 10                                    <TD>       2
<TR> <TD>   Outlet 11                                         <TD>  2
<TR> <TD>    Outlet 12 <TD>                                          2
<TR> <TD>    Outlet 13     <TD>                                      1
<TR> <TD>   *Outlet 14         <TD>                                  2
<TR> <TD>  *Outlet 15              <TD>                             1
<TR> <TD>    Outlet 16                 <TD>                          2
<TR> <TD>    Outlet 17                     <TD>                      2
<TR> <TD>    Outlet 18                         <TD>                  4
<TR> <TD>    Outlet 19                             <TD>              2
<TR>
</CENTER>
</TABLE>

<P>
Convention:
shoppers 0 - 9 belong to group 1,
shoppers 10 - 19 belong to group 2,
shoppers 20 - 29 belong to group 3, and
shoppers 30 - 39 belong to group 4
<P>

In each group, the first 5 shoppers make 3 visits and the remaining 5
shoppers make 4 visits. For example, in group 1, shoppers 0 - 4 make 3
visits and shoppers 5 - 9 make 4 visits.
<P> 

Besides, for the salesladies:
salesladies 0 - 1 belong to outlet 1,
salesladies 2 - 5 belong to outlet 2,
salesladies 6 belongs to outlet 3, 
... and
salesladies 33 - 34 belong to outlet 19.

</TT>


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